Dynamic-metamaterial coded-aperture imaging

1. A coded aperture sensing system, comprising: one or more electromagnetic (EM) detectors; a tunable coding aperture positioned relative to the one or more EM detectors and a plurality of voxels to scatter EM radiation traveling from the plurality of voxels towards the one or more EM detectors, the tunable coding aperture comprising: EM scattering elements spaced at less than or equal to half wavelength intervals, wherein the half wavelength intervals are half of an operational wavelength of the EM detectors; and tunable inputs operably coupled to the EM scattering elements and configured to adjust a coding matrix of the tunable coding aperture responsive to adjustments of controls applied to the tunable inputs; and control circuitry comprising a controller operably coupled to the tunable inputs, the controller programmed to: determine a desired aggregate coding matrix comprising an aggregation of a plurality of different desired coding matrices of the tunable coding aperture; determine a plurality of different control parameter vectors representing a plurality of different permutations of controls to be applied to the tunable inputs of the tunable coding aperture that will cause the coding matrix of the tunable coding aperture to adjust at least approximately to a different one of the plurality of desired coding matrices when applied to the tunable inputs of the tunable coding aperture; apply sequentially each of the plurality of different permutations of controls represented by the plurality of different control parameter vectors to the tunable inputs of the tunable coding aperture; and determine EM fields at each of the plurality of voxels at least in part as a function of EM fields detected at the one or more EM detectors responsive to each of the plurality of different permutations of controls being applied to the tunable inputs of the tunable coding aperture.

2. The coded aperture sensing system of claim 1 , wherein the plurality of voxels includes locations in space for which it is desired to infer amplitudes of the EM fields.

3. The coded aperture sensing system of claim 1 , wherein the plurality of voxels includes a plurality of pixels comprising locations in a two-dimensional manifold in space.

4. The coded aperture sensing system of claim 1 , wherein at least a portion of the plurality of voxels includes locations in space on or in one or more objects that it is desired to image.

5. The coded aperture sensing system of claim 1 , wherein the control circuitry is programmed to determine the desired aggregate coding matrix based, at least in part, on a coding matrix figure of merit of at least a portion of possible aggregate coding matrices of the tunable coding aperture.

6. The coded aperture sensing system of claim 5 , wherein the coding-matrix figure of merit includes an effective rank, the effective rank defined as a number of singular values of a matrix that exceed a predetermined threshold, wherein the desired aggregate coding matrix comprises one of the portion of possible aggregate coding matrices that has a highest effective rank.

7. The coded aperture sensing system of claim 5 , wherein the coding-matrix figure of merit includes a generalized determinant, the generalized determinant defined as a product of singular values of a matrix, wherein desired aggregate coding matrix comprising one of the portion of possible aggregate coding matrices that has a highest generalized determinant.

8. The coded aperture sensing system of claim 5 , wherein the coding-matrix figure of merit includes a minimum singular value, wherein the control circuitry is programmed to determine the desired aggregate coding matrix by selecting the desired aggregate coding matrix to be a matrix having a highest minimum singular value from among the at least a portion of possible aggregate coding matrices of the tunable coding aperture.

9. The coded aperture sensing system of claim 5 , wherein the coding-matrix figure of merit includes a condition number, wherein the control circuitry is programmed to determine the desired aggregate coding matrix by selecting the desired aggregate coding matrix to be a matrix having a lowest condition number from among the at least a portion of possible aggregate coding matrices of the tunable coding aperture.

10. The coded aperture sensing system of claim 5 , wherein the at least a portion of possible aggregate coding matrices of the tunable coding aperture includes at least a portion of possible aggregate coding matrices having a number N of aggregated coding matrices each.

11. The coded aperture sensing system of claim 10 , wherein the at least a portion of possible aggregate coding matrices having a number N of aggregated coding matrices includes all possible aggregate coding matrices of the tunable coded aperture having the number N of aggregated coding matrices.

12. The coded aperture sensing system of claim 10 , wherein the controller is programmed to select the number N to be a lowest integer that is greater than or equal to a number of the plurality of voxels divided by a number of the one or more EM detectors.

13. The coded aperture sensing system of claim 5 , wherein the at least a portion of possible aggregate coding matrices of the tunable coding aperture includes at least a portion of possible aggregate coding matrices having a number N+1 of aggregated coding matrices if it is determined that a matrix having a highest effective rank from among at least a portion of possible aggregate coding matrices having a number N of aggregated coding matrices is not full rank.

14. The coded aperture sensing system of claim 13 , wherein the at least a portion of possible aggregate coding matrices of the tunable coding aperture includes at least a portion of possible aggregate coding matrices having the number N of aggregated coding matrices if it is determined that the matrix having the highest effective rank from among the at least a portion of possible aggregate coding matrices having the number N of aggregated coding matrices is a full rank matrix.

15. The coded aperture sensing system of claim 5 , wherein the controller is programmed to determine the at least a portion of possible aggregate coding matrices as a function of at least a portion of possible control parameter vectors of the plurality of different control parameter vectors.

16. The coded aperture sensing system of claim 5 , wherein the controller is programmed to determine the at least a portion of possible aggregate coding matrices by modeling the tunable coding aperture to include lumped impedance elements corresponding to the EM scattering elements, the tunable inputs configured to enable selection of an impedance value for each of the lumped impedance elements.

17. The coded aperture sensing system of claim 16 , wherein the controller is programmed to: determine possible scattering matrices (S-matrices) relating field amplitudes at lumped ports for at least a portion of possible control parameter vectors, the lumped ports including: internal lumped ports located internally to the tunable coding aperture, each of the internal lumped ports corresponding to a different one of the lumped impedance elements of the tunable coding aperture; and external lumped ports located externally to the tunable coding aperture, each of the external lumped ports corresponding to a different one of the plurality of voxels or the one or more EM detectors; and determine the at least a portion of possible aggregate coding matrices using the determined possible S-matrices.

18. The coded aperture sensing system of claim 17 , wherein the controller is programmed to determine the possible S-matrices as functions of an impedance matrix (Z-matrix) and an admittance vector (y-vector), wherein the Z-matrix includes impedance values relating voltage potentials at each of the lumped ports to currents at each of the lumped ports with all others of the lumped ports open at an operational frequency of the EM detectors, and the y-vector is a diagonal matrix including admittance values of the lumped ports.

19. The coded aperture sensing system of claim 17 , wherein the controller is programmed to determine the possible S-matrices as functions of an admittance matrix (Y-matrix) and an impedance vector (z-vector), wherein the Y-matrix includes admittance values relating voltage potentials at each of the lumped ports to currents at each of the lumped ports with all others of the lumped ports open at an operational frequency of the EM detectors and the z-vector is a diagonal matrix including impedance values of the lumped ports.

20. The coded aperture sensing system of claim 1 , wherein a number of the one or more EM detectors is exactly one.

21. The coded aperture sensing system of claim 1 , wherein a number N of aggregated coding matrices of the desired aggregate coding matrix is at least a number of the one or more EM detectors.

22. A method of operating a coded aperture sensing system, the method comprising: scattering electromagnetic (EM) radiation traveling from a plurality of voxels towards one or more EM detectors with a tunable coding aperture including EM scattering elements spaced at less than or equal to half wavelength intervals; determining a desired aggregate coding matrix comprising an aggregation of a plurality of different desired coding matrices of the tunable coding aperture; determining a plurality of different control parameter vectors representing a plurality of different permutations of controls to be applied to tunable inputs of the tunable coding aperture that will cause the coding matrix of the tunable coding aperture to adjust at least approximately to a different one of the plurality of desired coding matrices when applied to the tunable inputs of the tunable coding aperture; applying sequentially each of the plurality of different permutations of controls represented by the plurality of different control parameter vectors to the tunable inputs of the tunable coding aperture; and determining EM fields at each of the plurality of voxels at least in part as a function of EM fields detected at the one or more EM detectors responsive to each of the plurality of different permutations of controls being applied to the tunable inputs of the tunable coding aperture.

23. The method of claim 22 , wherein scattering EM radiation traveling from a plurality of voxels towards one or more EM detectors with a tunable coding aperture includes scattering the EM radiation traveling from locations in space for which it is desired to infer amplitudes of the EM fields.

24. The method of claim 22 , wherein scattering EM radiation traveling from a plurality of voxels towards one or more EM detectors with a tunable coding aperture includes scattering the EM radiation traveling from locations in a two-dimensional manifold in space.

25. The method of claim 22 , wherein scattering EM radiation traveling from a plurality of voxels towards one or more EM detectors with a tunable coding aperture includes scattering the EM radiation traveling from locations in space on or in one or more objects that it is desired to image.

26. The method of claim 22 , wherein determining a desired aggregate coding matrix includes determining the desired aggregate coding matrix based, at least in part, on a coding matrix figure of merit of at least a portion of possible aggregate coding matrices of the tunable coding aperture.

27. The method of claim 26 , wherein determining the desired aggregate coding matrix based, at least in part, on a coding matrix figure of merit includes determining the desired aggregate coding matrix based, at least in part, on an effective rank of the at least a portion of possible aggregate coding matrices of the tunable coding aperture, the effective rank defined as a number of singular values of a matrix that exceed a predetermined threshold, wherein the desired aggregate coding matrix comprises one of the portion of possible aggregate coding matrices that has a highest effective rank.

28. The method of claim 26 , wherein determining the desired aggregate coding matrix based, at least in part, on a coding matrix figure of merit includes determining the desired aggregate coding matrix based, at least in part, on a generalized determinant of the at least a portion of possible aggregate coding matrices of the tunable coding aperture, the generalized determinant defined as a product of singular values of a matrix, wherein the desired aggregate coding matrix comprises one of the portion of possible aggregate coding matrices that has a highest generalized determinant.

29. The method of claim 26 , wherein determining the desired aggregate coding matrix based, at least in part, on a coding matrix figure of merit includes determining the desired aggregate coding matrix based, at least in part on a minimum singular value of the at least a portion of possible aggregate coding matrices of the tunable coding aperture, wherein determining the desired aggregate coding matrix includes selecting the desired aggregate coding matrix to be a matrix having a highest minimum singular value from among the at least a portion of possible aggregate coding matrices of the tunable coding aperture.

30. The method of claim 26 , wherein determining the desired aggregate coding matrix based, at least in part, on a coding matrix figure of merit includes determining the desired aggregate coding matrix based, at least in part on a condition number of the at least a portion of possible aggregate coding matrices of the tunable coding aperture, wherein determining the desired aggregate coding matrix includes selecting the desired aggregate coding matrix to be a matrix having a lowest condition number from among the at least a portion of possible aggregate coding matrices of the tunable coding aperture.

31. The method of claim 26 , wherein determining the desired aggregate coding matrix includes determining the desired aggregate coding matrix of the at least a portion of possible aggregate coding matrices of the tunable coding aperture including at least a portion of possible aggregate coding matrices having a number N of aggregated coding matrices each.

32. The method of claim 31 , wherein the at least a portion of possible aggregate coding matrices having a number N of aggregated coding matrices includes all possible aggregate coding matrices of the tunable coded aperture having the number N of aggregated coding matrices.

33. The method of claim 31 , further comprising selecting the number N to be a lowest integer that is greater than or equal to a number of the plurality of voxels divided by a number of the one or more EM detectors.

34. The method of claim 26 , wherein determining the desired aggregate coding matrix includes determining the at least a portion of possible aggregate coding matrices of the tunable coding aperture to include at least a portion of possible aggregate coding matrices having a number N+1 of aggregated coding matrices if it is determined that a matrix having a highest effective rank from among at least a portion of possible aggregate coding matrices having a number N of aggregated coding matrices is not full rank.

35. The method of claim 34 , further comprising determining the at least a portion of possible aggregate coding matrices of the tunable coding aperture to include at least a portion of possible aggregate coding matrices having the number N of aggregated coding matrices if it is determined that the matrix having the highest effective rank from among the at least a portion of possible aggregate coding matrices having the number N of aggregated coding matrices is a full rank matrix.

36. The method of claim 26 , wherein determining the desired aggregate coding matrix includes determining the at least a portion of possible aggregate coding matrices as a function of at least a portion of possible control parameter vectors of the plurality of different control parameter vectors.

37. The method of claim 26 , wherein determining the desired aggregate coding matrix includes modeling the tunable coding aperture to include lumped impedance elements corresponding to the EM scattering elements, the tunable inputs configured to enable selection of an impedance value for each of the lumped impedance elements.

38. The method of claim 37 , further comprising: determining possible scattering matrices (S-matrices) relating field amplitudes at lumped ports for at least a portion of possible control parameter vectors, the lumped ports including: internal lumped ports located internally to the tunable coding aperture, each of the internal lumped ports corresponding to a different one of the lumped impedance elements of the tunable coding aperture; and external lumped ports located externally to the tunable coding aperture, each of the external lumped ports corresponding to a different one of the plurality of voxels or the one or more EM detectors; and determining the at least a portion of possible aggregate coding matrices using the determined possible S-matrices.

39. The method of claim 38 , wherein determining possible S-matrices includes determining the possible S-matrices as functions of an impedance matrix (Z-matrix) and an admittance vector (y-vector), wherein the Z-matrix includes impedance values relating voltage potentials at each of the lumped ports to currents at each of the lumped ports with all others of the lumped ports open at an operational frequency of the EM detectors, and the y-vector is a diagonal matrix including admittance values of the lumped ports.

40. The method of claim 38 , wherein determining possible S-matrices includes determining the possible S-matrices as functions of an admittance matrix (Y-matrix) and an impedance vector (z-vector), wherein the Y-matrix includes admittance values relating voltage potentials at each of the lumped ports to currents at each of the lumped ports with all others of the lumped ports open at an operational frequency of the EM detectors and the z-vector is a diagonal matrix including impedance values of the lumped ports.

41. The method of claim 22 , wherein scattering EM radiation traveling from a plurality of voxels towards one or more EM detectors includes scattering the EM radiation towards a number of the one or more EM detectors that is exactly one.

42. The method of claim 22 , wherein determining a desired aggregate coding matrix comprising an aggregation of a plurality of different desired coding matrices of the tunable coding aperture includes determining the desired aggregate coding matrix to include a number N of the different desired coding matrices that is at least a number of the one or more EM detectors.